Sun Aug 25 12:18:19 1996

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Date: Sun, 25 Aug 1996 08:49:18 -0700
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From: "Robert B. Waltz" 
Subject: Re: Carbon dating
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On  Sat, 24 Aug 1996, REElliott@aol.com wrote:

[ ... ]
>
>For myself, coming from a medical (clinician) background, I have to agree
>with Robert's objections to this test in the textual critical arena.
>
>I ask two basic questions concerning C-14 dating:
>1. As for the testing procedure itself, where is a "control"?
>2. From a mathematical standpoint (and I'm no genius here) how does one solve
>an equation that has more than one variable, such as the one behind this
>method?
>
>If I'm wrong concerning the second question, please reply and show formulae.

Under certain circumstances, one *can* solve an equation with more
than one variable, by imposing other limits (Diophantine equations,
etc.).

But in the case of Carbon-14 dating, there is only one variable. I can't
give exact numbers (at least not easily; it's too much work to dig through
my CRC handbook). But I'll outline the process.

Carbon occurs in nature in three different isotopes: C-12, C-13, and
C-14. C-14 is radioactive; the others aren't. Since C-14 is generated
constantly, the supply in the atmosphere is (very nearly) constant.

Living things, by their very nature, are always taking in carbon.
(Plants take it in in the form of Carbon Dioxide; animals consume
sugars.) Since effectively all this carbon comes from the atmospehere,
living plants and animals have the same ration of C-12, C-13, and C-14
as the atmospehere does.

When a plant or animal dies, it stops taking in carbon. So from that
point on it ceases to replenish C-14 as it breaks down. So, over time,
the amount of C-14 breaks down, while the C-12 and C-14 remain behind.

Carbon-14 dating works by taking a sample of a once-living thing and
comparing the amounts of C-12, C-13, and C-14. The half-life of
C-14 is (I *think* -- this is the part I would have to look up) 1440
years. So after 1440 years, the amount of C-14 is exactly what it was
when the object died. After 2880 years, it is one-fourth. Etc. To
get the *theoretical* carbon date, one just finds the ratio of carbon
isotopes, then compares it with a graph of the C-14 decay rate. This
part is very easy (a lot easier than measuring the quantities of the
isotopes, which requires a very accurate mass spectrometer).

Which returns us to the problems: First, C-14 is so rare in nature that
it never constitutes more than a fraction of a percent of the total. So
even a highly accurate mass spectrometer has about a 5% error (hence the
inaccuracy of about a century in the findings). Second, the theoretical
scheme doesn't work. I don't know why, and neither does anybody else.
All dates have to be adjusted. And until we know *why*, it's hard to
be sure that we are perfectly accurate.

I hope this helps.

Bob Waltz
waltzmn@skypoint.com

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